Running a Correlation
Zora Parchman
2026-04-01
1 Loading Libraries
#install.packages("apaTables")
#install.packages("kableExtra")
library(psych) # for the describe() command and the corr.test() command
library(apaTables) # to create our correlation table
library(kableExtra) # to create our correlation table2 Importing Data
d <- read.csv(file="Data/projectdata.csv", header=T)
# For HW, import the your project dataset you cleaned previously; this will be the dataset you'll use throughout the rest of the semester3 State Your Hypothesis
There will be a significant relationship between Narcissistic Personality Inventory,Interpersonal Exploitativeness Scale, and Perceived Stress Questionnaire. Specifically, Narcissistic Personality Inventory will be positively related to Interpersonal Exploitativeness Scale and negatively related to Perceived Stress Questionnaire; and Interpersonal Exploitativeness Scale will be negatively related to Perceived Stress Questionnaire .
# you only need to check the variables you're using in the current analysis
# it's always a good idea to look them to be sure that everything is correct
str(d)## 'data.frame': 788 obs. of 7 variables:
## $ ResponseID: chr "R_12G7bIqN2wB2N65" "R_3lLnoV2mYVYHFvf" "R_1gTNDGWsqikPuEX" "R_2QLjdu3yoxqQ21c" ...
## $ race_rc : chr "white" "white" "white" "other" ...
## $ disability: chr "psychiatric" "other" "learning" "psychiatric" ...
## $ pipwd : num 2.33 2.33 3 2.93 3.33 ...
## $ npi : num 0.0769 0.7692 0 0.0769 0.6923 ...
## $ exploit : num 4.33 7 1.67 2.67 1.33 ...
## $ stress : num 4 3.5 4.4 3.6 3 3 3.7 3.4 2.7 3.8 ...# Since we're focusing only on our continuous variables, we're going to subset them into their own data frame. This will make some stuff we're doing later on easier.
d2 <- subset(d, select=c(stress, exploit, npi))
# You can use the describe() command on an entire dataframe (d) or just on a single variable (d$pss)
describe(d2)## vars n mean sd median trimmed mad min max range skew kurtosis
## stress 1 788 3.25 0.62 3.20 3.25 0.74 1.6 4.6 3 -0.06 -0.45
## exploit 2 788 2.34 1.32 2.00 2.17 1.48 1.0 7.0 6 0.98 0.52
## npi 3 788 0.28 0.30 0.15 0.24 0.23 0.0 1.0 1 0.88 -0.84
## se
## stress 0.02
## exploit 0.05
## npi 0.01# NOTE: Our fake variable has high kurtosis, which we'll ignore for the lab because we created it to be problematic. If you have high skew or kurtosis for any of your project variables, you will need to discuss it below in the Issues with My Data and Write up Results sections, as well as in your final project manuscript if your data does not meet the normality assumption.
# also use histograms to examine your continuous variables
# Because we are looking at 3 variables, we will have 3 histograms.
hist(d2$exploit)
hist(d2$stress)
hist(d2$npi)
# last, use scatterplots to examine your continuous variables together, for each pairing
# because we are looking at 3 variables, we will have 3 pairings/plots.
plot(d2$npi,d2$exploit)
plot(d2$npi,d2$stress)
plot(d2$exploit, d2$stress)
4 Check Your Assumptions
4.1 Pearson’s Correlation Coefficient Assumptions
- Should have 2 measurements for each participant.
- Variables should be continuous and normally distributed.
- Outliers should be identified and removed.
- Relationship between the variables should be linear .
4.1.1 Checking for Outliers
Note: For correlations, you will NOT screen out outliers or take any action based on what you see here. This is something you will simply check and then discuss in your write-up.We will learn how to removed outliers in later analyses.
# We are going to standardize (z-score) all of our 3 variables, and check them for outliers.
d2$npi <- scale(d2$npi, center=TRUE, scale=T)
hist(d2$npi)
sum(d2$npi < -3 | d2$npi > 3)## [1] 0d2$stress <- scale(d2$stress, center=TRUE, scale=T)
hist(d2$stress)
sum(d2$stress < -3 | d2$stress > 3)## [1] 0d2$exploit <- scale(d2$exploit, center=TRUE, scale=T)
hist(d2$exploit)
sum(d2$exploit < -3 | d2$exploit > 3)## [1] 74.2 Issues with My Data
All three of my variables meet all of the assumptions of Pearson’s correlation coefficient. One variable, Interpersonal Exploitativeness Scale had 7 outliers. Outliers can distort the relationship between two variables and sway the correlation in their direction. All three variable, Interpersonal Exploitativeness Scale,Perceived Stress Questionnaire,Narcissistic Personality Inventory also appears to have linear relationships with each other. Pearson’s r may underestimate the strength of a non-linear relationship and distort the relationship direction.The correlations should be evaluated carefully due to these risks.
5 Run a Single Correlation
corr_output <- corr.test(d2$exploit, d2$stress)6 View Single Correlation
corr_output## Call:corr.test(x = d2$exploit, y = d2$stress)
## Correlation matrix
## [,1]
## [1,] 0.06
## Sample Size
## [1] 788
## These are the unadjusted probability values.
## The probability values adjusted for multiple tests are in the p.adj object.
## [,1]
## [1,] 0.12
##
## To see confidence intervals of the correlations, print with the short=FALSE option7 Create a Correlation Matrix
corr_output_m <- corr.test(d2)8 View Test Output
corr_output_m## Call:corr.test(x = d2)
## Correlation matrix
## stress exploit npi
## stress 1.00 0.06 -0.01
## exploit 0.06 1.00 0.33
## npi -0.01 0.33 1.00
## Sample Size
## [1] 788
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## stress exploit npi
## stress 0.00 0.24 0.71
## exploit 0.12 0.00 0.00
## npi 0.71 0.00 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE option# Remember to report the p-values from the matrix that are ABOVE the diagonal!Remember, Pearson’s r is also an effect size! We don’t report effect sizes for non-sig correlations.
- Strong: Between |0.50| and |1|
- Moderate: Between |0.30| and |0.49|
- Weak: Between |0.10| and |0.29|
- Trivial: Less than |0.09|
9 Write Up Results
To test our hypothesis that Interpersonal Exploitativeness Scale,Perceived Stress Questionnaire,Narcissistic Personality Inventory would be correlated with one another, we calculated a series of Pearson’s correlation coefficients. All of the variables (Interpersonal Exploitativeness Scale,Narcissistic Personality Inventory,Perceived Stress Questionnaire) met the required assumptions of the test, with Narcissistic Personality and Perceived Stress Questionnaire meeting the standards of normality and containing no outliers. One variable, Interpersonal Exploitativeness Scale, had 7 outliers; so any significant results involving Interpersonal Exploitativeness Scale should be evaluated carefully .
As predicted, we found that all three variables were not significantly correlated (all ps were >.001). The effect size for Narcissistic Personality Inventory and Interpersonal Exploitativeness Scale was moderate, while the effect size between Stress and Narcissistic Personality Inventory and Perceived Stress Questionnaire with Interpersonal Exploitativeness Scale were both trivial; Cohen, 1988). Additionally, Narcissistic Personality Inventory was found to be negatively related to Interpersonal Exploitativeness Scale, but postively related to Perceived Stress Questionnaire which was postively related to Interpersonal Exploitativeness Scale which wasn’t predicted. Please refer to the correlation coefficients reported in Table 1.
| Variable | M | SD | 1 | 2 |
|---|---|---|---|---|
| Perceived Stress Questionnaire | 3.25 | 0.62 | ||
| Interpersonal Exploitativeness Scale | 2.34 | 1.32 | .06 | |
| [-.01, .12] | ||||
| Narcissistic Personality Inventory | 0.28 | 0.30 | -.01 | .33** |
| [-.08, .06] | [.27, .39] | |||
| Note: | ||||
| M and SD are used to represent mean and standard deviation, respectively. Values in square brackets indicate the 95% confidence interval. The confidence interval is a plausible range of population correlations that could have caused the sample correlation. | ||||
| * indicates p < .05 | ||||
| ** indicates p < .01. |
References
Cohen J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York, NY: Routledge Academic.